Phase dependent multimode interference device for coupled cavity lasers

ABSTRACT

A 3×3 multi-mode interference coupling device having a length L and a width W, a center input port between a pair of outer input ports, where each outer input port is displaced from the center input port by a distance W/3, and a center output port between a pair of outer output ports, where each outer output port is displaced from the center output port by a distance W/3, where the device is supports C bar , C cen , and a C x  coupling coefficients therein, when the outer input ports are equally excited with an input signal having a 180° phase difference, C cen  from each outer input port destructively interferes when the propagation length L is an integer number of L π /2, where the device outputs equal intensity laser modes from each outer output port when the propagation length is an integer multiple of L π /2.

FIELD OF THE INVENTION

The present invention relates generally to lasers. More specifically,the invention relates to optical waveguides involving multimodeinterference.

BACKGROUND OF THE INVENTION

In literature, examples of Multimode Interference devices (MMI) withequal and unequal splitting ratios for N inputs and M outputs are known.The reported geometries are optimized for switching applications but sofar little work on MMIs for coupled lasers has been performed. For thelatter a MMI is desirable where the two output signals have a 180° phasedifference, compared to the conventional 90°.

What is needed is a MMI device, which enables the integration of opticalfilters and widely tuneable laser architectures.

SUMMARY OF THE INVENTION

To address the needs in the art, a 3×3 multi-mode interference couplingdevice is provided that includes a length L and a width W, a centerinput port and a pair of outer input ports, where the center input portis disposed between the pair of outer input ports, where each outerinput port is displaced from the center input port by a distance W/3,and a center output port and a pair of outer output ports, where thecenter output port is disposed between the pair of outer output ports,where each outer output port is displaced from the center output port bya distance W/3 where the 3×3 multi-mode interference device is capableof supporting a C_(bar) coupling coefficient, a C_(cen) couplingcoefficient and a C_(x) coupling coefficient therein, where when thepair of outer input ports are equally excited with an input signal thathas a 180° phase difference, where the C_(cen) coupling coefficient fromeach outer input port destructively interferes when the propagationlength L is an integer multiple of L_(π)/2, where the 3×3 multi-modeinterference device outputs laser modes from each outer output port,where the output laser modes are of equal intensity when the propagationlength is an integer multiple of L_(π)/2.

According to one aspect of the invention, the length L includes a lengthof 5 Lπ/2, where C_(bar)≈0.78, C_(cen)≈0.57e^(jπ/3) and C_(bar)≈0.21e^(jπ).

In another aspect of the invention, the length L includes a length ofLπ/2, where C_(bar)≈0.21, C_(cen)≈0.57e^(jπ/3) and C_(x)≈0.78r^(jπ).

In one embodiment of the invention a 3×3 multi-mode interferencecoupling device is provided that includes a length L=5 Lπ/4 and a widthW, a pair of input/output ports, where each input/output port isdisplaced from a center axis by a distance W/3, and a reflectivesurface, where the reflective surface includes a planar surface that isdisplaced from the input ports by the length L=5 Lπ/4, where the 3×3multi-mode interference device is capable of supporting a C_(bar)coupling coefficient, a C_(cen) coupling coefficient and a C_(x)coupling coefficient therein, where when the pair of input/output portsare equally excited with an input signal that has a 180° phasedifference, the C_(cen), coupling coefficient from each pair ofinput/output ports destructively interferes, where the 3×3 multi-modeinterference device outputs laser modes from each pair of input/outputport, where the C_(bar)≈0.78, the C_(cen)≈0.57e^(jπ/3) and theC_(bar)≈0.21e^(jπ).

In one aspect of this embodiment, the reflective surface includes a pairof symmetric reflective surfaces disposed on opposite sides of thecentral axis, where the pair of symmetric reflective surfaces aredisposed at a 90-degree angle with respect to each other, where an apexof the 90-degree angle is along the central axis, where the lengthL=L_(π)/4, where C_(bar)≈0.78 C_(cen)≈0.57 e^(jπ/3) andC_(x)≈0.21e^(jπ).

BRIEF DESCRIPTION OF T DRAWINGS

FIGS. 1A-1D show (FIG. 1A) 3×3 MMI geometry, (FIG. 1B) a BPM simulationof single input excitation of MMI, (FIG. 1C) excitation of the MMI witha 180 degree phase difference, and (FIG. 1D) related MMI couplergeometry with excluded middle waveguide, according to one embodiment ofthe current invention.

FIG. 2 shows a graph of the normalized power in each output port of thecoupling MMI reflector shown in FIG. 1D, as a function of the phasedifference between the inputs, according to one embodiment of thecurrent invention.

FIGS. 3A-3B show (FIG. 3A) 3×3 MMI geometry having a flat mirror at 5L_(π)/4, and (FIG. 3B) excitation of the MMI a having 180 degree phasedifference showing the beat length 5 L_(π)/4, according to oneembodiment of the invention.

FIG. 4 shows a coupled cavity laser formed by using the reflector shownin FIG. 1D, according to one embodiment of the invention.

FIGS. 5A-5B show a comparison between a conventional MichelsonInterferometer (FIG. 5A) and an interferometer formed using the MMIreflector shown in FIG. 1D, according to one embodiment of theinvention.

FIG. 6 shows a simulated spectral response of the conventional Michelsoninterferometer shown in FIG. 5A vs. the interferometer formed using theMMI reflector shown in FIG. 5B, according to the current invention.

FIG. 7 shows a widely tunable coupled cavity laser formed using MMIreflector shown in FIG. 1D, according to the current invention.

FIG. 8 shows a schematic diagram of the tuning principle of a coupledcavity, according to one embodiment of the invention.

FIG. 9A shows a schematic diagram of the integrated coupled cavity laserin FIG. 7 with an interferometer in one cavity using two MMI reflectorsshown in FIG. 1D, according to one embodiment of the invention.

FIG. 9B shows a schematic diagram of the mode selection of theintegrated coupled cavity laser with an interferometer in FIG. 9A,according to one embodiment of the invention.

FIG. 10 shows a ring coupled cavity laser, according to one embodimentof the invention.

FIGS. 11A-11B show spectral results of a fabricated coupled cavitylaser, according to one embodiment of the invention.

DETAILED DESCRIPTION

The current invention is a Multimode Interference device (MMI), whichenables the realization of new integrated optical filters and widelytuneable laser architectures. According to one embodiment, thefabrication is based on UV-Lithograpy, which makes the laser especiallyattractive for low-cost applications in telecommunication and sensing.Embodiments of the invention are also compatible with any genericintegration platform for photonic integrated circuits. Further, one ormore waveguides are connected to a significantly wider multimodewaveguide. According to one embodiment, a set of modes inside the widermultimode waveguide are excited by placing the inputs at predefinedpositions. The superposition of the excited modes leads to periodicimaging of the input fields after propagating through the multimodesection. The type of images and periodicity depends strongly on the setof excited modes. In literature examples with equal and unequalsplitting ratios for N inputs and M outputs are well explained. Thereported geometries are optimized for switching applications but so farlittle work on MMIs for coupled lasers has been performed. For thelatter the MMI of the current invention outputs two signals that have a180° phase difference, compared to the conventional 90°.

One embodiment of the current invention includes a 3×3 generalinterference MMI in transmission as shown in FIG. 1A. The 3×3 geometryproduces images of equal intensity at the beat length L_(π). Here, theguided-mode propagation method (MPA) is used to illustrate theself-imaging effect on the MMI device. In this aspect, the propagationconstants β_(i) (I=0, 1, 2, 3, . . . , N, where N is the number ofguided modes) of the multi-modes in the MMI area are given in theparaxial approximation by:

${\beta_{0} - \beta_{i}} \eqsim \frac{{i\left( {i + 2} \right)}\pi}{3L_{\pi}}$where L_(π) is defined as the beat length (or coupling length) betweenthe fundamental mode (i=0) and the first-order mode (i=1):

${L_{\pi} \equiv \frac{\pi}{\beta_{0} - \beta_{1}}} = \frac{4n_{r}W_{e}^{2}}{3\lambda}$where λ is the free-space wavelength and W_(e) is the effective width ofthe MMI area:

$W_{e} \eqsim {W + {\frac{\lambda}{\pi}\left( \frac{n_{c}}{n_{r}} \right)^{2\sigma}\text{/}\sqrt{n_{r}^{2} - n_{c}^{2}}}}$where W is the physical width of the MMI area, n_(r) and n_(c) are theeffective core index and effective cladding index, respectively; andinteger σ=0 for TE modes and σ=1 for TM modes.

In FIG. 1B, shown is a numerical example of the propagation inside themultimode section of one embodiment of the current invention, where L isindicated. Here it is seen that at L_(π)/2 three images are present withunequal intensities such that C_(bar)≈0.21, C_(cen)≈0.57 e^(jπ/3) andC_(x)≈0.78e^(jπ). By realizing that the phase difference between C_(x)and C_(bar) is 180°, a 2×2 coupler in the 3×3 geometry is provided whenthe central waveguide is excluded. Although this implies a significantimaging loss in general, no light is lost if the two outer inputs aresimultaneously excited with almost equal intensities and a phasedifference of 180°. Here, destructive interference occurs in the centraloutput at multiples of L_(π)/2, as can be seen in FIG. 1C.

The amplitude coupling coefficients differ in each multiple of L_(π)/2.According to the current invention, six different possible solutionsexist for the amplitude coupling coefficients and are shown in Table 1.For larger values of L, the coefficients repeat.

TABLE 1 Coupling Coefficients for different length of the 3 × 3 MMILength Coefficients L_(π)/2 C_(bar) ≈ 0.21, C_(cen) ≈ 0.57e^(jπ/3) andC_(x) ≈ 0.78e^(jπ). L_(π) C_(bar) ≈ 0.57, C_(cen) ≈ 0.57e_(j) ^(π) andC_(x) ≈ 0.57e^(1.33jπ). 3L_(π)/2 C_(bar) ≈ 0.7, C_(cen) ≈ 0 and C_(x) ≈0.7e^(1.5jπ). 2L_(π) C_(bar) ≈ 0.57, C_(cen) ≈ 0.57e^(−0.33jπ) and C_(x)≈ 0.57e^(−1.33jπ). 5L_(π)/2 C_(bar) ≈ 0.78, C_(x) ≈ 0.57e^(jπ/3) andC_(bar) ≈ 0.21e^(jπ). 3L_(π) C_(bar) ≈ 0, C_(x) ≈ 0 and C_(bar) ≈1e^(2jπ).

In one embodiment, a fully reflective device is obtained by placing acorner mirror at half the distances reported in Table 1, as indicated inFIG. 1D. Due to the corner reflection, the coupling coefficients areinterchanged. Note that ideal values reported in the table above onlyoccur in reflection when the two input intensities are equal and theirphase difference is 180°. For all other phase differences the imaging asshown in FIG. 1C is not optimal and a loss will occur. This propertymakes the current embodiment of the invention also a phase dependentreflector. The normalized reflection for each input port is depicted inFIG. 2 for different phase differences between inputs.

In another embodiment, a fully reflective device is obtained by placinga flat mirror at 5 L_(π)/4, as indicated in FIG. 3A, where the device is5-times longer (see FIG. 3B) than the device shown in FIG. 1D. Again,the ideal values reported in the Table 1 above only occur in reflectionwhen the two input intensities are equal and their phase difference is180°. This property makes the current embodiment of the invention also aphase dependent reflector.

According to aspects of the embodiments of the invention, the twocoupled cavities are coupled in a way, that little light is exchangedbetween them, e.g. C_(x)<C_(bar), with a relative phase of (π), as shownin Table 1, where the coupling coefficients are summarized for a 3×3 MMIin transmission as shown in FIG. 1A. □□ Here, the proper couplingcoefficients are only attainable for length of 5 Lπ/2 and repetition of3 L_(π).

Other embodiments of the invention include a 3×3 MMI with a length ofLπ/2, where the limitation of C_(x)>C_(bar) is overcome by implementingthe cavities such that they physically cross each other. □Further, a MMIreflector of this device is enabled if the length is halved andterminated with the corner reflective surface shown in FIG. 1D. Here,the corner reflector exchanges/inverts the coupling coefficients suchthat C_(x′) becomes C_(bar) and C_(bar′) becomes C_(x), where a coupledFabry-Perot geometry is enabled. □□

Turning now to some exemplary applications of these devices, whereFabry-Perot coupled cavity lasers are shown in FIG. 4. According to thisexemplary implementation of the invention, a laser is formed by couplingtwo multimode laser cavities to create a single tuneable laser. This isbased on the Vernier Effect. The coupling is done using the couplingmirror shown in FIG. 1D. According to further aspects of the invention,the MMI is used to couple two cavities such as Fabry-Perot CoupledCavity Lasers, interferometer based on the MMI reflector, a Widelytunable Coupled Cavity laser, a Laser design with two internal cavityfilters, and a Ring Coupled Cavity laser, or one Fabry-Perot and onering. □

An integrated Michelson Inteferometer is provided in FIG. 5A. In afurther exemplary implementation, using the phase dependent reflectionof the embodiment in FIG. 1D, an optical filter based on a MichelsonInterferometer can be formed as shown in FIG. 5B. By using the fact thatthe component mainly reflects for a 180° phase difference between thetwo inputs, every second peak of the periodic Michelson response issuppressed (see FIG. 6). This enhances the effective Free Spectral Rangeof the optical filter by a factor of two, without changing the spectralwidth of the filter or the footprint. This ultimately doubles the tuningrange in lasers employing similar interferometers.

Turning now to extended coupled cavity laser designs using the currentinvention, where two laser cavities (see FIG. 7), that by themselvesemit multiple wavelengths, are coupled together through the mirror asshown in FIG. 1D. In this exemplary application, the cavities havedifferent lengths and one of them may contain a wavelength dependentadjustable mirror (e.g. interferometer). The laser wavelength can befine-tuned by means of current injection in one of the cavities andcoarsely tuned when the effective mirror is altered, as shown in FIG.9A.

The final lasing mode selection can be explained as follows. The gridspacing between two possible lasing modes within Laser 1 and Laser 2 ofFIG. 7 and FIG. 9A depends on the length of the individual laser. Chosenslightly different, the coupling enforces a lasing wavelength where bothgrids coincide.

According to the embodiment of FIG. 7 and FIG. 9A, if current isinjected in one of the lasers, the laser can be tuned, as the twopossible lasing grids are shifted with respect to each other. However,as the two grids are periodic, they might overlap also at a secondwavelength further away. This usually limits the overall tuning range.To distinguish between the desired wavelength and an unwanted copy, awavelength dependent filter is employed in one of the cavities. Bytuning this mirror one of the remaining possibilities can be selected.This effect is illustrated schematically in FIG. 8 and FIG. 9B, wherethe bold lines represent the final lasing mode.

The mode selection mechanism is shown in FIG. 9B. The Vernier effectbetween the two cavities, with a FSR determined by ΔL₁ and the cavitylength, is used for selecting one wavelength from the Fabry-Perot combspectrum. The imbalance ΔL₂ is chosen to suppress the competingwavelength one FSR away from the target mode in cavity 2. Consequently,the coupled system operates on the FSR, which coincides with the maximumreflection of the interferometer. Coarse tuning is accomplished via φ₂,with a range determined by the choice of ΔL₂. The fine selection isachieved by adjusting the longitudinal modes of the cavities using thephase sections φ₁. During this process a photo current is generated onthe detector, with a magnitude related to the selected longitudinalmode. The lasing mode, which coincides with the interferometerreflection peak produces the smallest current. In this way the laser canbe stabilized by minimizing the detector current.

According to the embodiment shown in FIG. 7 and FIG. 9A, a widelytunable coupled cavity laser based on a Michelson Interferometer withdoubled Free Spectral Range is provided. Shown are two coupledFabry-Perot cavities with a length difference ΔL_(I), each containing anamplifier (SOA) and a phase tuning section φ₁. The two cavities arecoupled via a 2-Port MIR coupling mirror, which introduces a 180° phaseshift between its ports instead of the usual 90°. This is essential toensure the wavelength selection with high SMSR. One cavity contains atunable interferometer with imbalance ΔL₂ and phase sections φ₂, whichrestricts the effective round trip gain bandwidth and allows coarsewavelength tuning. The other cavity is forming by a cleaved waveguidetermination R₁. The 2×2 Multimode Interference splitter at the input ofthe interferometer, is connected with one port to an integrated photodetector which is used for stability control. The reflection spectrum ofthe interferometer is similar to a Michelson interferometer, but itprovides precisely twice the Free Spectral Range (FSR), whilemaintaining the same Full-Width-Half maximum (FWHM).

A prototype using 4 mm long cavities coupled together (where 2 mm arephase shifters) has been fabricated. The device is fully functional with9 mW coupled to a lensed fiber. Typical spectral results are displayedin FIGS. 11A-11B, with SMSR above 40 dB and tunability of above 25 nm.

Turning now to a ring coupled cavity laser, where a Fabry-Perot cavityis coupled to a Ring. The structure is shown in FIG. 10. The couplingdevice used for this structure is 5 L_(π)/2 long, as reported inTable 1. The benefit of this structure is the possibility to use aneffective reflection coating as mirror. This is an excellent alternativefor platforms with poor integrated mirrors. Alternatively, theFabry-Perot cavity can also be replaced by a ring, or the ring by aFabry-Perot Cavity.

The present invention has now been described in accordance with severalexemplary embodiments, which are intended to be illustrative in allaspects, rather than restrictive. Thus, the present invention is capableof many variations in detailed implementation, which may be derived fromthe description contained herein by a person of ordinary skill in theart. For example a two ring-coupled laser, a two Fabry Perot type laser,or a mix of those. The effective mirror can be realized by any type ofinterferometer as e.g. Mach-Zehnders, Michelson, Ring Resontaors butalso devices with a wavelength-dependent insertion loss as e.gmultiplexers as Arrayed-Waveguide gratings or Echelle gratings. Furtherthe device might be used to couple multiple cavities together, as e.g.three or four cavities.

All such variations are considered to be within the scope and spirit ofthe present invention as defined by the following claims and their legalequivalents.

What is claimed:
 1. A two port phase dependent reflective multi-modeinterference coupling device comprising: a) a multimode waveguide havinga length L=5 Lπ/4 and a width W, wherein said length Lπ is a couplinglength between a fundamental optical mode (i=0) and a first order mode(i=1) according to${{L_{\pi} \equiv \frac{\pi}{\beta_{0} - \beta_{1}}} = \frac{4n_{t}W_{e}^{2}}{3\lambda}},$wherein β₀ and β₁ are propagation constants of the multimodes, wherein λis the free-space wavelength and W_(e) is the effective width of themultimode waveguide area${W_{e} \approx {W + {\frac{\lambda}{\pi}{\left( \frac{n_{c}}{n_{r}} \right)^{2\sigma}/\sqrt{n_{r}^{2} - n_{c}^{2}}}}}},$wherein said W is the physical width of said multimode waveguide area,wherein n_(r) is the effective core index of said multimode waveguide,wherein n_(c) is the effective cladding index of said multimodewaveguide, wherein integer σ=0 for TE modes and σ=1 for TM modes; b) apair of input/output ports, wherein each said input/output port isdisplaced from the center axis of said multimode waveguide by a distanceW/3, wherein said two port reflective multi-mode interference device iscapable of supporting a C_(bar) coupling coefficient and a C_(x)coupling coefficient therein; and c) a reflective surface, wherein saidreflective surface comprises a planar surface that is displaced fromsaid input/output ports by said length L=5 Lπ/4, wherein saidC_(bar)≈0.78, and said C_(x)≈0.21e^(jπ), wherein when said pair ofinput/output ports are simultaneously excited with two input signalsthat have 180° phase difference and equal intensity said two port phasedependent reflective multi-mode interference device outputs signals withmaximum intensity, wherein when each one of laser modes from two lasersare connected simultaneously to each one of said pair of input/outputports, each one of said laser modes coincide with a maximum reflectionintensity of said reflective multi-mode interference device.
 2. A twoport phase dependent reflective multi-mode interference coupling deviceof claim 1, wherein said reflective surface comprises a pair ofsymmetric reflective surfaces disposed on opposite sides of said centralaxis, wherein said pair of symmetric reflective surfaces are disposed ata 90-degree angle with respect to each other, wherein an apex of said90-degree angle is along said central axis, wherein said lengthL=L_(π)/4, wherein said C_(bar)≈0.78, and said C_(x)≈0.21e^(jπ).